A Grocery Chain Is Considering the Installation of a Set

question 107

Essay

A grocery chain is considering the installation of a set of 4 self-checkout lanes.The new self-checkout lane setup will replace 2 old cashier lanes that were staffed by a cashier and bagger on each lane.One cashier mans all 4 self-checkouts (answering questions,checking for un-scanned items,taking coupons,etc).Checkout on the new lanes takes 2 minutes (customers bag their own orders)while checkout with the old lanes took only 45 seconds.In addition the electricity costs for both setups are $0.05 per checkout while bagging (material)costs are $0.10 per checkout with the old system and $0.15 for the new system.The new lanes also require $100 in capital costs.Assume that the lanes are always in use for 8 hours per day (1 shift)and that a worker makes $10/hour.
(a)How many checkouts did the old system provide in a shift?
(b)How many checkouts does the new system provide?
(c)What is the multifactor productivity for each system?

---

Definitions:

Range

The difference between the highest and lowest values in a data set, indicating the span of data points.

Standard Deviation

A measure of the dispersion or variability within a set of numerical data, indicating how spread out the values are from the mean.

Variance

A statistical measure of the dispersion representing how much the data points in a data set diverge from the mean value.

Mean

The arithmetic average of a set of numbers, calculated by adding them all together and dividing by the number of numbers.